Here are some leads/checks you can do, and sequence to follow; I'm assuming the checks you've done on the units were on the workbench.
Fuse 13 in the main fuse box could be the one, power to the control unit (ECU) is supplied via the ignition key switch and from the line fuse supplying the pump.
Power to the pump is supplied by the 30Amp fuse found near the battery terminal, see pic in post:
https://www.acownersclub.co.uk/forum/index.php?topic=8494.30 page 3.
You can check both power feeds by removing the relay mounted beside the ECU, see pic attached. Mine is marked "214" with an Audi symbol, its a WAG part common
on Audis, scrapyards here seem to be full of them (143 hits).
My roof does not always lower when the engine runs (why I wonder?)
Make sure the manual release catch is pushed in to the locked position.
For "roof down" my vehicle has to be in neutral with the handbrake on and the ignition on
without the engine running to work (9 times out of 10).
The red light should come on when the roof is unlocked and the hood front lifted to the position where it doesn't drop down.
The windows should drop down about 2 inches too (only the passenger window drops on my vehicle).
There is only one light to my knowledge, though I seem to remember a mention of lights on the ECU unit from somewhere....
For "roof up" same procedure except I can usually run the engine.
I don't think the Thatcham ignition disabler has to be switched into start engine mode to operate the roof.
/Paho